Marcelina uses a blend of white corn and yellow corn to make tortilla chips at her restaurant. She needs to buy

Can anybody help plzz?? 65 points

Yakvenalex [24]

Answer:

$\frac{dy}{dx} =\frac{-8}{x^2} +2$

$\frac{d^2y}{dx^2} =\frac{16}{x^3}$

Stationary Points: See below.

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Calculus

Derivative Notation dy/dx

Derivative of a Constant equals 0.

Stationary Points are where the derivative is equal to 0.

1st Derivative Test - Tells us if the function f(x) has relative max or mins. Critical Numbers occur when f'(x) = 0 or f'(x) = undef
2nd Derivative Test - Tells us the function f(x)'s concavity behavior. Possible Points of Inflection/Points of Inflection occur when f"(x) = 0 or f"(x) = undef

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Quotient Rule: $\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}$

Step-by-step explanation:

Step 1: Define

$f(x)=\frac{8}{x} +2x$

Step 2: Find 1st Derivative (dy/dx)

Quotient Rule [Basic Power]: $f'(x)=\frac{0(x)-1(8)}{x^2} +2x$
Simplify: $f'(x)=\frac{-8}{x^2} +2x$
Basic Power Rule: $f'(x)=\frac{-8}{x^2} +1 \cdot 2x^{1-1}$
Simplify: $f'(x)=\frac{-8}{x^2} +2$

Step 3: 1st Derivative Test

Set 1st Derivative equal to 0: $0=\frac{-8}{x^2} +2$
Subtract 2 on both sides: $-2=\frac{-8}{x^2}$
Multiply x² on both sides: $-2x^2=-8$
Divide -2 on both sides: $x^2=4$
Square root both sides: $x= \pm 2$

Our Critical Points (stationary points for rel max/min) are -2 and 2.

Step 4: Find 2nd Derivative (d²y/dx²)

Define: $f'(x)=\frac{-8}{x^2} +2$
Quotient Rule [Basic Power]: $f''(x)=\frac{0(x^2)-2x(-8)}{(x^2)^2} +2$
Simplify: $f''(x)=\frac{16}{x^3} +2$
Basic Power Rule: $f''(x)=\frac{16}{x^3}$

Step 5: 2nd Derivative Test

Set 2nd Derivative equal to 0: $0=\frac{16}{x^3}$
Solve for x: $x = 0$

Our Possible Point of Inflection (stationary points for concavity) is 0.

Step 6: Find coordinates

Plug in the C.N and P.P.I into f(x) to find coordinate points.

x = -2

Substitute: $f(-2)=\frac{8}{-2} +2(-2)$
Divide/Multiply: $f(-2)=-4-4$
Subtract: $f(-2)=-8$

x = 2

Substitute: $f(2)=\frac{8}{2} +2(2)$
Divide/Multiply: $f(2)=4 +4$
Add: $f(2)=8$

x = 0

Substitute: $f(0)=\frac{8}{0} +2(0)$
Evaluate: $f(0)=\text{unde} \text{fined}$

Step 7: Identify Behavior

See Attachment.

Point (-2, -8) is a relative max because f'(x) changes signs from + to -.

Point (2, 8) is a relative min because f'(x) changes signs from - to +.

When x = 0, there is a concavity change because f"(x) changes signs from - to +.

3 0

3 years ago

(1 point) Find y as a function of x if

Alenkasestr [34]

Y’’(x)= 6x + 1
y’(x)= 3x^2 + x + 2
y(x)= x^3 + 1/2x^2 + 2x + 5

7 0

1 year ago

How can a model help you solve surface area and volume problems

romanna [79]

A model shows the visualize of what you need to do in order to complete the problem your asked. It can also show important steps and make it easier for you to answer the question, like length×height×width.

4 0

3 years ago

Simplify (x⁴)³ ??????

Morgarella [4.7K]

Rule:

(xᵃ)ᵇ = x⁽ᵃ * ᵇ⁾

(x⁴)³ = x⁽⁴ * ³⁾ = x¹²

3 0

2 years ago

Someone plz help me with this plz

kolezko [41]

Answer:

NOt finished

Step-by-step explanation:

PAGE 1

1.) enlargement b/c the number is more that 1

2.) reduction b/c the number is less than 1

3.) enlargement b/c the number is more than 1

4.) reduction b/c the number is less than 1

5.) reduction k = 1/3

6.) enlargement k = 5/2 or 2.5

PAGE 2

7.) reduction k = 1/3

8.) enlargement k = 2

PAGE 3

Screen shot

PAGE 4

screen shot

PAGE 5

screen shot

I WILL DO THE SCREENSHOTS TOMORROW

7 0

2 years ago